Barls, yes you could do this, it will syphon as long as the full keg is higher than the bottom one.
I have done this a few times, takes ages, but you can then just leave it once its started syphoning.
FIRST, start with the full keg sitting well above the empty keg (higher).
Loosen the relief valve in the empty keg.
Purge the filter, lines and empty keg with co2 as doc said.
Then use very low co2 pressure to prime the ciruit with beer, bleeding air out of the filter housing until its full of beer.
Then set the relief valve in the empty keg so you hear it hissing, and you are sure the beer is flowing thru.
Then disconnect the gas line into the full keg.
Then close the relief valve in the empty keg, it should be syphoning now.
Then connect a line between the 2 kegs, onto each of the gas fittings.
The beer will syphon, and the gas from the empty keg will return into the full one.
If you carefully prime the full system with co2, and do it at a syphon pace instead of blowing it thru with gas pressure, you will have less chance of oxygenation (if thats a word), and you wont use too much co2.
And being able to leave it once its started is a bonus.
cheers,
Chris